1. Amaldi 9 Cardiff University 10-15 July 2011 Parameter estimation for LISA Pathfinder Giuseppe Congedo University of Trento for the LTPDA team

2. Outline of the talk  LISA Pathfinder concept & system identification  Parameter estimation I.Monte Carlo validation II.Robustness to non-standard scenarios  Optimal design of experiments  Impact of parameter estimation on residual force noise 14/07/2011Giuseppe Congedo - Amaldi 92

3. LISA Pathfinder concept 14/07/2011Giuseppe Congedo - Amaldi 93 LISA one-way Doppler link LISA Pathfinder  study the link in terms of residual force disturbances  prove free fall within 3x10 -14 m s -2 Hz -1/2 around 1 mHz  measure and characterize the residual force noise M. Hewitson talk on “The LISA Pathfinder Mission”

4. Controlled dynamics 14/07/2011Giuseppe Congedo - Amaldi 94 LISA Pathfinder measurement scheme  TM 1 in free fall along x  SC follows TM 1, through µN-thruster actuation  TM 2 follows TM 1, through electrostatic actuation TM 1 TM 2 SC x electrostatic actuators o 12 o1o1 µN-thrusters o 1 = IFO(x 1 ) o 12 = IFO(x 12 )

5. TM 1 TM 2 Control scheme & system parameters 14/07/2011Giuseppe Congedo - Amaldi 95 IFO x1x1 x 12 o1o1 o 12 S 21 C df A df Δt 1 C sus A sus Δt 2 ω12ω12 ω22ω22  ω 1 2, ω 12 2 =ω 2 2 -ω 1 2 : spring-like couplings between the SC and each TM, [~-1x10 -6 s -2 ]  S 21 : sensing cross-talk between o 1 and o 12, [~ 1x10 -4 ]  A df, Δt 1 : actuation gain and delay for the application of thruster forces [~ 1, < 1 s]  A sus, Δt 2 : actuation gain and delay for the application of electrostatic suspension forces [~ 1, < 1 s]

6. System identification experiments  LISA Pathfinder is a multi-input/multi- output dynamical system  We inject frequency sweeps spanning 0.1 – 50 mHz 14/07/2011Giuseppe Congedo - Amaldi 96 Exp. 1 o i,1 TM 1 TM 2 IFO x1x1 x 12 o1o1 o 12 S 21 C df A df Δt 1 C sus A sus Δt 2 ω12ω12 ω 12 2 Exp. 2 o i,12

7. Parameter estimation 14/07/2011Giuseppe Congedo - Amaldi 97 IFO noise data Whitening filters IFO sys. id. exps. data Model templates Whitened data Whitened templates System parameters M. Nofrarias poster on “Parameter estimation in LISA Pathfinder operational exercises” 3 methods: linear with SVD, non-linear, MCMC

8. Monte Carlo validation: parameter statistics 14/07/2011Giuseppe Congedo - Amaldi 98  Estimation is unbiased for all 7 parameters  Uncertainties are in agreement with Fisher matrix Mean best-fit True value Standard deviation of the mean

9. Parameter correlation 14/07/2011Giuseppe Congedo - Amaldi 99

10. Parameter correlation 14/07/2011Giuseppe Congedo - Amaldi 910

11. Monte Carlo validation: loglikelihood chains 14/07/2011Giuseppe Congedo - Amaldi 911 1000 iterations altogether Noise perturbes the chains a lot

12. Monte Carlo validation: loglikelihood statistics 14/07/2011Giuseppe Congedo - Amaldi 912 Statistical removal of deterministic part

13. Robustness to the initial guess: performance 14/07/2011Giuseppe Congedo - Amaldi 913  Strongly uncalibrated system, low thruster performance, unexpected force couplings  Estimation was able to reach the true values within ~1 sigma, from 10 3 -10 4 sigmas

14. Robustness to the initial guess: analysis of residuals 14/07/2011Giuseppe Congedo - Amaldi 914

15. Robustness to glitches 14/07/2011Giuseppe Congedo - Amaldi 915 excess noise at high frequency  Failures in the electronics, nonlinearities, unexpected phenomena, etc.  Simulation of SG glitches  We are still able to recover the true parameters with “some care”

16. Optimal design of LISA Pathfinder experiments 14/07/2011Giuseppe Congedo - Amaldi 916 System parameters (ω 1, ω 12, S 21,...) Injection parameters (frequencies and amplitudes) Results:  Improvement of up to 1 order of magnitude in parameter precision  Minimezed parameter correlations  Fewer sine frequencies to inject

17. Estimation of residual force noise 14/07/2011Giuseppe Congedo - Amaldi 917 factor 4 improvement around 0.4 mHz factor 2 improvement around 50 mHz

18. Final comments  Monte Carlo simulation has proven self-consistency  Robust with respect to the initial guess and glitches  Applied to operational exercises with a realistic black-box ESA simulator  Experiments can be optimized to get better precision in all parameters  Parameter estimation is mandatory to avoid systematics in the assessment of residual force noise for all space-based GW missions 14/07/2011Giuseppe Congedo - Amaldi 918

19. Thanks for your attention! 14/07/2011Giuseppe Congedo - Amaldi 919

20. Additional slides... 14/07/2011Giuseppe Congedo - Amaldi 920

21. Equation of motion 14/07/2011Giuseppe Congedo - Amaldi 921 total residual force noise Input control forces LISA Pathfinder eom in freq. domain sensing forces dynamics readoutcoord.s inputs controller... for system identification... for estimation of out-of-loop residual force noise